The pedigree shows a family in which sickle-cell anaemia appears…

The parents in generation I. II-1 is affected, $\text{Hb}^\text{S}\text{Hb}^\text{S}$, but her parents are not. So I-1 and I-2 are both carriers, $\text{Hb}^\text{A}\text{Hb}^\text{S}$.

(a) II-3. A carrier × carrier cross gives $\text{Hb}^\text{A}\text{Hb}^\text{A} : \text{Hb}^\text{A}\text{Hb}^\text{S} : \text{Hb}^\text{S}\text{Hb}^\text{S} = 1 : 2 : 1$. II-3 is unaffected, so he is one of the first $3$ parts, and $2$ of them are carriers: $\dfrac{2}{3} = 66.7\%$.

(b) II-4. Her father I-3 is affected and can give her only $\text{Hb}^\text{S}$. She is unaffected, so her other allele is $\text{Hb}^\text{A}$: she is a carrier for certain, $100\%$.

(c) III-1 affected. III-1 can be affected only if II-3 is a carrier ($\frac{2}{3}$); then a carrier × carrier child is affected with a chance of $\frac{1}{4}$: $\dfrac{2}{3} \times \dfrac{1}{4} = \dfrac{1}{6} = 16.7\%$.

(d) III-1 a carrier. If II-3 is $\text{Hb}^\text{A}\text{Hb}^\text{A}$ ($\frac{1}{3}$), a child of him and II-4 is a carrier with a chance of $\frac{1}{2}$. If II-3 is a carrier ($\frac{2}{3}$), a child is again a carrier with a chance of $\frac{1}{2}$ ($\frac{2}{4}$). So the chance is $\dfrac{1}{2} = 50\%$ either way.

(e) Two affected children. Both children can be affected only if II-3 is a carrier, and then each child is affected with a chance of $\frac{1}{4}$: $\dfrac{2}{3} \times \dfrac{1}{4} \times \dfrac{1}{4} = \dfrac{1}{24} = 4.17\%$.